Existential threats to the US homeland have come in many forms – some real, some imagined. There was immigration from Asia – referred to in the xenophobic phrase “yellow peril” – fascism in Europe, communism in the Soviet Union and radical Islam in the Middle East.

And now there is Justin Trudeau in Canada.

The new Canadian prime minister’s plan to fast track his country’s intake of Syrian refugees was scrutinised on Wednesday by the US Senate homeland security committee, amid fears that it will enable terrorists to cross the border and reach US soil. Trudeau will make a state visit to Washington next month.

The hearing, which did not begin with a rendition of the song Blame Canada from South Park, offered a glimpse of the relationship between the US and its northern neighbour, once characterised by Trudeau’s father Pierre, a previous prime minister, as like “sleeping with an elephant”.

It also raised the possibility that Republican candidate Donald Trump chose the wrong border when he promised to build a wall to keep out people from Mexico. The northern border, it transpires, is far more porous.

The committee was told that of 21,000 agents in the US border patrol, only 2,100 are assigned to the northern border, with probably only about 300 of those guarding it at any one time. Witness Dean Mandel of the US National Border Patrol Council said: “I would assess that there are approximately as many Capitol police on duty right now protecting the Capitol complex as we have on the entire 4,000-mile northern border.”

On the shorter southern border with Mexico, he added, there is one agent for every linear mile. On the northern border with Canada, there is one agent for every 13.5 miles and much less infrastructure. And the number of Canadian agents on the other side is probably even fewer.

Can we expect President Trump to order Trudeau to erect a border wall? There would be practical problems, for a start. Many people cross by boat and the technology that greets them is far from cutting edge.

Witness Dr Laura Dawson, director of the Canada Institute at the Wilson Center in Washington, said: “We’ve got great lakes and great fishing and hundreds of miles of the border is actually under water. I don’t know how you build a wall under water. We’ve got pieces of the border that stretch through mountains.”

It may surprise some to know that the primary concern of those worried about the Canadian border is not about hordes of Americans pouring over the border in search of inexpensive healthcare. During his election campaign, Trudeau made the ambitious pledge to resettle 25,000 refugees fleeing the violence in Syria by the end of 2015. This has been delayed slightly to the end of this month. The move was lauded by progressives and liberals as typical of Canadian humanitarianism. Among US Republicans, not so much.

Senator Rob Portman of Ohio warned: “If Canada is accelerating that programme, that puts us more at risk.”

Senators questioned whether security would be compromised by overworked Canadian officials failing to vet the refugees properly through background checks. Witness Guidy Mamann, a Canadian legal expert, said they would be under pressure to get the job done for Trudeau: “This was the crown jewel of his election platform. This is a mark he has to hit.”

Witness David Harris, director of the international intelligence programme at Insignis Strategic Research in Ottawa, told the committee that, taking the relative population sizes into account, the 25,000 refugees in Canada would be the equivalent of 255,000 refugees in the US. “Britain, almost twice Canada’s population, will take several years to admit 20,000,” he added.

“If the extensive US intelligence system would have trouble security-screening 10,000 Syrians in a year, how likely is it that Canada, even with valuable US assistance, could adequately screen two and a half times that number in four months?”

But Dawson mounted a spirited defence of the Canadian policy. She said refugees coming to the country were from low risk groups – families with children, single mothers, and lesbians, gay, bisexual and transgender people – all of whom have taken refuge in Jordan, Lebanon and Turkey. Some 60% are women and 22% are children. “This is not an Isis demographic,” she said.

While 25,000 is a big number, it is consistent with Canada’s response to historic crises: before it gained independence, it was a haven for African Americans fleeing slavery in the US. “Canadians looked at the images of Aylan Kurdi, the little boy on the beach this summer, and said this is not who we are. We are a community of diversity, we are a community who accepts newcomers.”

Senator Tom Carper, ranking member on the committee, offered a different, intriguing theory for Canadian kindness: too much space. With a population of just 35m and a vast land mass, he suggested, it needs more people.

Mandel, meanwhile, suggested the refugee resettlement was something of a red herring compared with the 5 million foreign visitors who enter Canada each year. He described its visa waiver system as “a huge security gap”. He also called for more staff, resources and cooperation.

Yet through it all, the unfailingly polite American senators – many from border states including New Hampshire – went out of their way to flatter their friends in the north, saying how often they had been to Canada, how they had Canadian friends, how they even got mistaken for Canadians. “I love Canadians,” said chairman Ron Johnson, who goes fishing up there.

As the hearing drew to a close, senator Jon Tester of Montana told his colleagues and the Canadian witnesses that the US must accept responsibility for the refugee situation. “We invaded Iraq 15 years ago looking for weapons of mass destruction. The result of that has been quite frankly the Middle East is a mess. These refugees don’t have any homes, they’ve been destroyed.

“The best way to radicalise people is not to reintegrate them into a society. We have an obligation to figure out how to do this and do this right for the sake of this country, but we cannot ignore it because if we do, we’re not doing anybody any favours on this earth.”

Perhaps emboldened by this, it was Dawson who supplied the zinger of the day: “Without being cute, the United States is more of a risk to Canada than Canada is to the United States.”